How to scale only one side of a mesh/scale unevenly?
You can use Proportional Editing for that. Go into Edit mode and enable Proportional Editing (the button in the toolbar at the bottom - click it and set 'Enabled') and set it to Linear mode (the selection will appear once you've enabled Proportional Editing). It should look like this :



Then select the vertices at the end of the mesh that you want to scale. Press S to scale. Drag them to the size you want and then scroll the mouse wheel (or equivalent) to change the range of the proportional edit tool until you have the desired influence.



I've purposefully used a cylinder with a number of loop cuts in the image above to demonstrate how the rest of the mesh is affected by the proportional edit.